# How do you factor 216x^3+1?

Mar 24, 2017

$\left(6 x + 1\right) \left(36 {x}^{2} - 6 x + 1\right)$

#### Explanation:

This is a $\textcolor{b l u e}{\text{sum of cubes}}$ which is factorised, in general, as

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$216 {x}^{3} + 1 = {\left(6 x\right)}^{3} + {1}^{3}$

$\Rightarrow a = 6 x \text{ and } b = 1$

$\Rightarrow 216 {x}^{3} + 1 = \left(6 x + 1\right) \left(36 {x}^{2} - 6 x + 1\right)$